Branched Polymers and Dimensional Reduction
John Z. Imbrie (Virginia)
Abstract:
I will describe an exact relation between self-avoiding branched
polymers in D+2 continuum dimensions and the hard-core continuum
gas at negative activity in D dimensions (see [math-ph/0107005
and 0203055]). Our results explain why the critical behavior of
branched polymers should be the same as that of the i\phi^3 (or
Yang-Lee edge) field theory in two fewer dimensions (as proposed
by Parisi and Sourlas in 1981). I will review conjectures and
results on critical exponents for D+2=2,3,4 and show that they
are corollaries of our result. I will also discuss dimensional
reduction for directed branched polymers.